![]() ![]() Definition of the definite integral ∑ƒ(ci)∆xi, as ∆x→0 FUNDAMENTAL THEOREM OF CALCULUS TURN UP DRANK FADED MILLI BILLI BEAN ∫ƒ(x)dx from a to b = F(b) - F(a), where F is an antiderivative of ƒ Mean Value Theorem / Average value of a function ∫ƒ(x)dx from a to b = ƒ(c)(b-a) Differential equation An equation involving the derivative(s) of a function. ∫ƒ(x)dx = F(x) + C, since all functions of the form F(x) + C satisfy (F(x) + C)' = ƒ(x). Antiderivative A function F(x) that satisfies F'(x) = ƒ(x) Definition of the indefinite integral The collection of all antiderivatives of a function, e.g. Inflection point A point where ƒ" changes from positive to negative or vice versa. Local minimum/maximum A point where ƒ' changes from positive to negative or vice versa. Points tested for minima/maxima Critical points and enpoints. Critical number A number c is called critical if ƒ'(c) = 0 or ƒ is not differentiable at c. ![]() Extreme Value Theorem If ƒ is continuous on a closed interval, then ƒ has both a minimum and maximum on the interval. Definition of a maximum ƒ(c) is the maximum of ƒ on an interval if ƒ(c) ≥ f(x) for all x contained in the interval.
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